CF1671D.Insert a Progression

You are given a sequence of $n$ integers $a_1, a_2, \dots, a_n$. You are also given $x$ integers $1, 2, \dots, x$.

You are asked to insert each of the extra integers into the sequence $a$. Each integer can be inserted at the beginning of the sequence, at the end of the sequence, or between any elements of the sequence.

The score of the resulting sequence $a'$ is the sum of absolute differences of adjacent elements in it $\left(\sum \limits_{i=1}^{n+x-1} |a'_i - a'_{i+1}|\right)$.

What is the smallest possible score of the resulting sequence $a'$?

给你一个长度为 $n$ 的整数序列 $a_1, a_2, \dots, a_n$，以及 $x$ 个额外的整数：$1, 2, \dots, x$。

你需要将这 $x$ 个额外整数逐一插入到序列 $a$ 中。每次插入时，可选择将其放在序列开头、结尾，或任意两个元素之间。

设插入后得到的序列为 $a'$，其得分定义为相邻元素间绝对差值之和，即

$$\sum_{i=1}^{n+x-1} |a'_i - a'_{i+1}|。$$

请问：所得序列 $a'$ 的最小可能得分是多少？

The first line contains a single integer $t$ ($1 \le t \le 10^4$) — the number of testcases.

The first line of each testcase contains two integers $n$ and $x$ ($1 \le n, x \le 2 \cdot 10^5$) — the length of the sequence and the number of extra integers.

The second line of each testcase contains $n$ integers $a_1, a_2, \dots, a_n$ ($1 \le a_i \le 2 \cdot 10^5$).

The sum of $n$ over all testcases doesn't exceed $2 \cdot 10^5$.

第一行包含一个整数 $t$（$1 \le t \le 10^4$）—— 测试用例的数量。

每个测试用例的第一行包含两个整数 $n$ 和 $x$（$1 \le n, x \le 2 \cdot 10^5$）—— 序列的长度以及额外整数的个数。

每个测试用例的第二行包含 $n$ 个整数 $a_1, a_2, \dots, a_n$（$1 \le a_i \le 2 \cdot 10^5$）。

所有测试用例中 $n$ 的总和不超过 $2 \cdot 10^5$。

For each testcase, print a single integer — the smallest sum of absolute differences of adjacent elements of the sequence after you insert the extra integers into it.

对于每个测试用例，输出一个整数——在将额外的整数插入序列后，序列中相邻元素绝对差之和的最小值。

Here are the sequences with the smallest scores for the example. The underlined elements are the extra integers. Note that there exist other sequences with this smallest score.

• $\underline{1}, \underline{2}, \underline{3}, \underline{4}, \underline{5}, 10$
• $\underline{7}, 7, \underline{6}, \underline{4}, 2, \underline{2}, \underline{1}, \underline{3}, \underline{5}, \underline{8}, 10$
• $6, \underline{1}, 1, \underline{2}, 5, 7, 3, 3, 9, 10, 10, 1$
• $1, 3, \underline{1}, 1, 2, \underline{2}, \underline{3}, \underline{4}, \underline{5}, \underline{6}, \underline{7}, \underline{8}, \underline{9}, \underline{10}$

以下是示例中得分最小的序列。下划线标出的元素为额外整数。注意，存在其他具有相同最小得分的序列。

• $\underline{1}, \underline{2}, \underline{3}, \underline{4}, \underline{5}, 10$
• $\underline{7}, 7, \underline{6}, \underline{4}, 2, \underline{2}, \underline{1}, \underline{3}, \underline{5}, \underline{8}, 10$
• $6, \underline{1}, 1, \underline{2}, 5, 7, 3, 3, 9, 10, 10, 1$
• $1, 3, \underline{1}, 1, 2, \underline{2}, \underline{3}, \underline{4}, \underline{5}, \underline{6}, \underline{7}, \underline{8}, \underline{9}, \underline{10}$